Answer
$[-4,2)$
Work Step by Step
Step 1. Rewrite the inequality as
$\frac{x}{x+2}-2\geq0$
which gives
$\frac{x-2x-4}{x+2}\geq0$, $\frac{-x-4}{x+2}\geq0$, and $\frac{x+4}{x+2}\leq0$
Thus the boundary points are $x=-4,-2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-4)...(-)...(-2)...(+)...$
Thus the solutions are $-4\leq x\lt-2$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $[-4,2)$
